DOCSLIB.ORG

Modeling Techniques

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modeling Techniques Appendix A Modeling Techniques A.1 Population Growth Models Using Differential Equations Our main goal here is to introduce a few modeling techniques we use throughout this book. We do not intend however to provide here the fundamentals on modeling, a tutorial or a review. For these, we refer to other sources (DeAngelis et al. 1992; Ford 2009; Grimm et al. 2006; Kuang 1993). This Appendix is rather a refresher as well as an example of why using different modeling techniques for one and the same problem can be beneficial to understand biological processes better. We start with the simple exponential population growth to make modeling accessible even to complete beginners. Biologists generally define a population as a collection of individuals that belong to the same species and can potentially breed with each other. One of the best-known early models on population growth was outlined by Malthus (1798). He famously maintained that the human population is predicted to grow in an exponential manner, but the crucial products needed to sustain the population grow in but a linear manner. He argued that these different types of growths will trigger disasters when the population’s needs are not satisfied. The basic exponential growth model consists of a single positive feedback loop that arises from the fact that every individual (N) is predicted to have a fixed number of offspring (r), regardless of the size of the population, and thus also regardless of the remaining resources in the habitat: dN = rN dt (A.1.1) This exponential growth model had a profound effect on biology such as developing the theory of natural selection (Darwin 1859). Exponential population growth is physically not possible in the long run, because either the resources needed to sustain the growth run out (e.g., space, nutrients, access to light, etc.) or due to density-dependent factors, such as the rate of individuals’ access to food, © Springer Nature Switzerland AG 2020 149 I. Karsai et al., Resilience and Stability of Ecological and Social Systems, https://doi.org/10.1007/978-3-030-54560-4 150 A Modeling Techniques the dependence of infection on population density, or the density dependence of fertility rates. These will have an increasing effect as the population grows in size. In real populations thus also a negative feedback loop is found within the system that counteracts the positive feedback loop which drives exponential growth. The population usually avoids catastrophe via moderating its own growth as the population increases and the interplay of these two feedback loops also makes the population resilient against perturbations. This general pattern has been observed also in chemistry and it was described by the Belgian mathematician Verhulst (1845) as the density-dependent dynamics of chemical reactions, which led to the best- known early population model: dN N = rN − dt 1 K (A.1.2) The beauty of this simple equation is that the actual reproduction rate scales linearly between a maximum value (r) and minimum value of zero—or, if a population becomes by some force larger than its habitat’s carrying capacity (K), it can even have negative values leading to a decline of the population. No reproduction happens any more when the population reaches its carrying capacity (N = K). This is a simple equation that can be solved formally to predict population size at any time in a closed form, if the maximum reproductive rate (r), carrying capacity (K), and the initial population size (N0) are given: KN ert N(t) = 0 rt (A.1.3) K + N0(e − 1) Many models in biology have further complexities such as time delays or a large number of other parameters, therefore the actual model equations often cannot be solved formally. In such cases, we can still perform numerical simulations which, with some caveat, will give us still useful predictions and insights into the properties of the system. Many programming languages and modeling platforms have built-in equation solvers. One of the best-known examples for numerical simulations was developed by the school of “System Dynamics” (Forrester 1968) which led to simulation tools like Stella or Vensim (Eberlein and Peterson 1992). The advantage of the systems dynamics approach is that it combines visual sketches that demonstrate the causal relations between the system’s components with the mathematical functions needed to solve models (Fig. A.2). Vensim requires the user to clearly establish the logical connections of the model (by doing sketching). The complicated differential equations are dissected into inflows and outflows, which make debugging easier and only require elemental algebra to plug in the rates. A Vensim system can show results in tables or figures (Fig. A.1). A Modeling Techniques 151 Fig. A.1 Predicted population size per unit area (acres, using the scale given) for a plant growing as the Verhulst equation describes it in Vensim. Parameters: N0 = 10, r = 0.8andK = 1000 Fig. A.2 Vensim model of sigmoid growth as in the Verhulst equation. The box called “stock” where the quantities (in this case the individuals belonging to the population) are stored. This stock integrates the flows (double arrow). This model has one inflow term called “growth” which funnel the individuals from the source (small cloud) to the stock. This flow contains a rate equation which have 3 inputs and is expressed as an algebraic term: rN(K − N/K) A.2 Agent-Based Models of Population Growth Without analyzing the sigmoid growth model and its biological importance in details, we also need to mention that the cited assumptions of r and K are biologically quite unrealistic. They are not constants and they actually summarize several other important life history parameters. Generally, the two most common ways to resolve these problems are either to include more parameters and variables into the model (as we did in Chap. 2) or using an altogether different model design, where these parameters are actually missing in the specification of the model but will emerge in runtime. 152 A Modeling Techniques Fig. A.3 Starting configuration of an agent-based Netlogo model. Trees and animals have their own rule sets and several parameters of the model are actually variables and their values are different for each individual. Agents can move and interact with each other and with the environment while updating key variables such as energy level. This energy level in turn, affects the agents’ behavior (die of hunger, breed and so on) Models using aggregated parameters and equations have a top-down design. A different, bottom-up design for modeling populating growth would be to use cybernetic models (urn or cellular automata models, agent-based i.e., individual- based models) such as implemented in Netlogo (Wilensky 1999). For example, in an agent-based model for population growth, each agent has an energy level which is a state of the current energy budget calculated from spending and gaining energy tokens by the behavior of that individual. Movement and reproduction cost energy, while feeding gains energy. In this approach, reproduction rate will not be a constant parameter, but depend, as a simple emergent property, on this energy dynamics. The same is true for carrying capacity: It is not programmed directly into the system, but will depend on factors such as how quickly the agents find food, how much they can exploit food that is present, and how the food regenerates. We show in details such energy-based ecological microcosms (Chaps. 2 and 3), but the main idea for these agent- or individual-based models is to simulate population growth where the aggregate (biologically unrealistic) parameters are replaced by a simple life history (i.e., a mechanism) with dynamic elements. The agent-based models can also predict a sigmoid growth without directly implementing r and K (Fig. A.3). Rather, K and r will be emergent properties of the system (Figs. A.4 and A.5). While the above two modeling approaches have very different structures, assumptions, and presentations, their predictions are very close. (The agent-based model can be downloaded1). To summarize, in this book we wanted to emphasize that different modeling approaches of the same problems can give the same but also different insights and understandings. It is important to have different perspectives. Practical questions also play an important role. For example, agent-based models can run for a long 1https://sites.google.com/site/springerbook2020/chapter-4. A Modeling Techniques 153 1800 Individuals Na = 100 Na = 200 Na = 400 Na = 800 Na = 1600 0 200 400 600 800 1000 1400 020406080100 Years Fig. A.4 Sigmoid population growth predicted by the agent-based model without using the Verhulst equation and the parameters r and K. Left panel: a single run as shown on the modeling platform; Right panel: processed data: average value of 20 runs of the animal population at different starting values (N0). Reprinted from Karsai et al. (2016) with permission from Elsevier A B Individuals Reproduction rate Na = 100 Na = 200 Na = 400 Na = 800 Na = 1600 0 200 400 600 800 1000 1200 1400 1600 0.0 0.1 0.2 0.3 0.4 0.5 51015200 20 40 60 80 100 Ye a r s Years Fig. A.5 Estimated population parameters from the agent-based model (numbers are calculated from the result data and was not part of the model itself); (A) Change of reproductive rate of animals; (B) emergent stable population size (K) of the animals at different starting conditions. Reprinted from Karsai et al. (2016) with permission from Elsevier time and needed to have multiple runs and statistical evaluations. This may not be very practical for the cases when quick results are needed.
Load more

Recommended publications
  • Density Dependence in Demography and Dispersal Generates Fluctuating
    Density dependence in demography and dispersal generates fluctuating invasion speeds Lauren L. Sullivana,1, Bingtuan Lib, Tom E. X. Millerc, Michael G. Neubertd, and Allison K. Shawa aDepartment of Ecology, Evolution and Behavior, University of Minnesota, Saint Paul, MN 55108; bDepartment of Mathematics, University of Louisville, Louisville, KY 40292; cDepartment of BioSciences, Program in Ecology and Evolutionary Biology, Rice University, Houston, TX 77005; and dBiology Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 Edited by Alan Hastings, University of California, Davis, CA, and approved March 30, 2017 (received for review November 23, 2016) Density dependence plays an important role in population regu- is driven by reproduction and dispersal from high-density pop- lation and is known to generate temporal fluctuations in popu- ulations behind the invasion front (13–15)]. The conventional lation density. However, the ways in which density dependence wisdom of a long-term constant invasion speed is widely applied affects spatial population processes, such as species invasions, (16, 17). are less understood. Although classical ecological theory suggests In contrast to classic approaches that emphasize a long-term that invasions should advance at a constant speed, empirical work constant speed, there is growing empirical recognition that inva- is illuminating the highly variable nature of biological invasions, sion dynamics can be highly variable and idiosyncratic (18–25). which often exhibit nonconstant spreading speeds, even in sim- There are several theoretical explanations for fluctuations in ple, controlled settings. Here, we explore endogenous density invasion speed (which we define here as any persistent tem- dependence as a mechanism for inducing variability in biologi- poral variability in spreading speed), including stochasticity in cal invasions with a set of population models that incorporate either demography or dispersal (24–28) and temporal or spatial density dependence in demographic and dispersal parameters.
    [Show full text]
  • Plant Diversity Increases with the Strength of Negative Density Dependence at the Global Scale
    RESEARCH FOREST ECOLOGY predators, pathogens, or herbivores) and/or com- petition for space and resources (2–4, 7). Numer- ous studies have documented the existence of CNDD in one or several plant species (8–12), and Plant diversity increases with the most of these studies explicitly or implicitly as- sume that stronger CNDD maintains higher spe- strength of negative density cies diversity in communities. However, only a handful of studies have explicitly examined dependence at the global scale the link between CNDD and species diversity (4, 11, 13, 14),andnostudyhasexaminedthis relationship across temperate and tropical lat- Joseph A. LaManna,1,2* Scott A. Mangan,2 Alfonso Alonso,3 Norman A. Bourg,4,5 itudes. Despite decades of study, our understand- Warren Y. Brockelman,6,7 Sarayudh Bunyavejchewin,8 Li-Wan Chang,9 ing of how processes at local scales—such as Jyh-Min Chiang,10 George B. Chuyong,11 Keith Clay,12 Richard Condit,13 density-dependent biotic interactions—influence Susan Cordell,14 Stuart J. Davies,15,16 Tucker J. Furniss,17 Christian P. Giardina,14 18 18 19,20 global patterns of biodiversity remains in flux I. A. U. Nimal Gunatilleke, C. V. Savitri Gunatilleke, Fangliang He, 1 15 21 22 23 ( , ). Robert W. Howe, Stephen P. Hubbell, Chang-Fu Hsieh, Both species-specific and more generalized 14 24 25 15,16 Faith M. Inman-Narahari, David Janík, Daniel J. Johnson, David Kenfack, mechanisms can cause CNDD, but only CNDD 3 24 26 17 Lisa Korte, Kamil Král, Andrew J. Larson, James A. Lutz, caused by species-specific mechanisms can main- 27,28 4 29 Sean M.
    [Show full text]
  • "Density Dependence and Independence"
    Density Dependence and Advanced article Independence Article Contents . Introduction: Concepts and Importance in Ecology Mark A Hixon, Oregon State University, Corvallis, Oregon, USA . Mechanisms of Density Dependence . Old Debates Resolved Darren W Johnson, Oregon State University, Corvallis, Oregon, USA . Detecting Density Dependence . Future Directions Online posting date: 15th December 2009 Density dependence occurs when the population growth parameter of interest involves population dynamics, rate, or constituent gain rates (e.g. birth and immi- including the population growth rate and the four primary gration) or loss rates (death and emigration), vary caus- demographic (or vital) rates – birth, death, immigration ally with population size or density (N). When these and emigration – although related parameters, such as growth and fecundity, are also investigated. See also: parameters do not vary with N, they are density-inde- Population Dynamics: Introduction pendent. Direct density dependence, where the popu- Use of the words ‘density dependence’ alone normally lation growth rate or gain rates vary as a negative means ‘direct density dependence’ (or compensation): the function of N, or the loss rates vary as a positive function of per capita (proportional) gain rate (population or indi- N, is necessary but not always sufficient for population vidual growth, fecundity, birth or immigration) decreases regulation. The opposite patterns, inverse density as N increases (Figure 1a) or the loss rate (death and/or dependence or the Allee effect, may push endangered emigration) increases as N increases (Figure 1b). The populations towards extinction. Direct density depend- opposite patterns are called inverse density dependence (or ence is caused by competition, and at times, predation.
    [Show full text]
  • Literature Cited in Lizards Natural History Database
    Literature Cited in Lizards Natural History database Abdala, C. S., A. S. Quinteros, and R. E. Espinoza. 2008. Two new species of Liolaemus (Iguania: Liolaemidae) from the puna of northwestern Argentina. Herpetologica 64:458-471. Abdala, C. S., D. Baldo, R. A. Juárez, and R. E. Espinoza. 2016. The first parthenogenetic pleurodont Iguanian: a new all-female Liolaemus (Squamata: Liolaemidae) from western Argentina. Copeia 104:487-497. Abdala, C. S., J. C. Acosta, M. R. Cabrera, H. J. Villaviciencio, and J. Marinero. 2009. A new Andean Liolaemus of the L. montanus series (Squamata: Iguania: Liolaemidae) from western Argentina. South American Journal of Herpetology 4:91-102. Abdala, C. S., J. L. Acosta, J. C. Acosta, B. B. Alvarez, F. Arias, L. J. Avila, . S. M. Zalba. 2012. Categorización del estado de conservación de las lagartijas y anfisbenas de la República Argentina. Cuadernos de Herpetologia 26 (Suppl. 1):215-248. Abell, A. J. 1999. Male-female spacing patterns in the lizard, Sceloporus virgatus. Amphibia-Reptilia 20:185-194. Abts, M. L. 1987. Environment and variation in life history traits of the Chuckwalla, Sauromalus obesus. Ecological Monographs 57:215-232. Achaval, F., and A. Olmos. 2003. Anfibios y reptiles del Uruguay. Montevideo, Uruguay: Facultad de Ciencias. Achaval, F., and A. Olmos. 2007. Anfibio y reptiles del Uruguay, 3rd edn. Montevideo, Uruguay: Serie Fauna 1. Ackermann, T. 2006. Schreibers Glatkopfleguan Leiocephalus schreibersii. Munich, Germany: Natur und Tier. Ackley, J. W., P. J. Muelleman, R. E. Carter, R. W. Henderson, and R. Powell. 2009. A rapid assessment of herpetofaunal diversity in variously altered habitats on Dominica.
    [Show full text]
  • STAGE STRUCTURE, DENSITY DEPENDENCE and the EFFICACY of MARINE RESERVES Colette M. St. Mary, Craig W. Osenberg, Thomas K. Frazer
    BULLETIN OF MARINE SCIENCE, 66(3): 675–690, 2000 STAGE STRUCTURE, DENSITY DEPENDENCE AND THE EFFICACY OF MARINE RESERVES Colette M. St. Mary, Craig W. Osenberg, Thomas K. Frazer and William J. Lindberg ABSTRACT The habitat requirements of fishes and other marine organisms often change with on- togeny, so many harvested species exhibit such extreme large-scale spatial segregation between life stages that all life stages cannot be protected within a single marine reserve. Nevertheless, most discussions of marine reserves have focused narrowly on single life- history events (e.g., reproduction or settlement) or a single life stage (e.g., adult or re- cruit). Instead, we hypothesize that an effective marine reserve system should often in- clude a diversity of protected habitats, each appropriate to a different life stage. In such a case, the spatial configuration of habitats within reserves, and of separate reserves across larger spatial scales, may affect how marine resources respond to reserve design. We explored these issues by developing a mathematical model of a fish population consist- ing of two benthic life stages (juvenile and adult) that use spatially distinct habitats and examined the population’s response to various management scenarios. Specifically, we varied the sizes of reserves protecting the two life stages and the degree of coupling between juvenile and adult reserves (i.e., the fraction of the protected juvenile stock that migrates into the adult reserve upon maturation). We examined the effects when density dependence operated in only the juvenile stage, only the adult stage, or both. The results demonstrated that population stage structure and the nature of density dependence should be incorporated into the design of marine reserves but did not provide robust support for the general tenet that all life stages must be protected for an effective reserve system.
    [Show full text]
  • DENSITY DEPENDENCE, the LOGISTIC EQUATION, and R- AUD
    89 DENSITY DEPENDENCE,THE LOGISTIC EQUATION, AND r- AUD K-SELECTION: A CRITIQUE AI{D AN AJ,TERNATIVEAPPROACH Jan Kozlowski Department of Animal Ecology Jagiellonlan University Karasia 6 30-060 Krak6w, POLAND Received September 18,1978; July 9, 1980 ABSTRACT: The logistic equation is a starting point of many ecological theories. Most ecologists agree that this equation is usually not conslstent Iillth observations and experlmental results but it ls argued that the slmpllclty of fhis equatlon ls the reason for this lnconsistency. In this paper I attempt to prove that the reason for inadequacy of the logistic equation l-s more fundamental: most systems qf equa- tions descrlbing the dynamlcs of population and lts resources cannot be transformed to the single equatlon for limited growth. Even if thls transformation is posslble' the K parameter depends on components of !r usually on the ratLo of mortallty rate to reproduction rate. Thls fact ls commonly overlooked because it ls assuned that denslty affects the abstract term r (popul-atlon growth rate). Because of doubts as to density-dependence and the logistlc equation, the r- and K-selectlon concept is criticLzed, both as a classiflcation system and as a predlctlve theory. It ls shown that when resources are explicltly consldered, it ls possible to prediet traits favored by natural- selectLon on a given resource level dlrectly from the descrlptlon of the system. This approach seems to be more advan- tageous than the r- and K-selection concept. I. INTRODUCTION Ttre logistic equation is a mathematical formulation of the denslty-dependent facEors concept. Though density-dependence may no longer be a burning issue lt ls dlfflcult to flnd a contemporary ecology textbook that does not contaln the loglstlc equation.
    [Show full text]
  • Drechslerella Stenobrocha Genome Illustrates the Mechanism Of
    Liu et al. BMC Genomics 2014, 15:114 http://www.biomedcentral.com/1471-2164/15/114 RESEARCH ARTICLE Open Access Drechslerella stenobrocha genome illustrates the mechanism of constricting rings and the origin of nematode predation in fungi Keke Liu1,2†, Weiwei Zhang1,2†, Yiling Lai1,2, Meichun Xiang1, Xiuna Wang1, Xinyu Zhang1 and Xingzhong Liu1* Abstract Background: Nematode-trapping fungi are a unique group of organisms that can capture nematodes using sophisticated trapping structures. The genome of Drechslerella stenobrocha, a constricting-ring-forming fungus, has been sequenced and reported, and provided new insights into the evolutionary origins of nematode predation in fungi, the trapping mechanisms, and the dual lifestyles of saprophagy and predation. Results: The genome of the fungus Drechslerella stenobrocha, which mechanically traps nematodes using a constricting ring, was sequenced. The genome was 29.02 Mb in size and was found rare instances of transposons and repeat induced point mutations, than that of Arthrobotrys oligospora. The functional proteins involved in nematode-infection, such as chitinases, subtilisins, and adhesive proteins, underwent a significant expansion in the A. oligospora genome, while there were fewer lectin genes that mediate fungus-nematode recognition in the D. stenobrocha genome. The carbohydrate-degrading enzyme catalogs in both species were similar to those of efficient cellulolytic fungi, suggesting a saprophytic origin of nematode-trapping fungi. In D. stenobrocha, the down-regulation of saprophytic enzyme genes and the up-regulation of infection-related genes during the capture of nematodes indicated a transition between dual life strategies of saprophagy and predation. The transcriptional profiles also indicated that trap formation was related to the protein kinase C (PKC) signal pathway and regulated by Zn(2)–C6 type transcription factors.
    [Show full text]
  • Counterintuitive Density-Dependent Growth in a Long-Lived Vertebrate After Removal of Nest Predators Ricky-John Spencer Iowa State University
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Digital Repository @ Iowa State University Ecology, Evolution and Organismal Biology Ecology, Evolution and Organismal Biology Publications 12-2006 Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Ricky-John Spencer Iowa State University Fredric J. Janzen Iowa State University, [email protected] Michael B. Thompson University of Sydney Follow this and additional works at: http://lib.dr.iastate.edu/eeob_ag_pubs Part of the Evolution Commons, and the Population Biology Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ eeob_ag_pubs/151. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Ecology, Evolution and Organismal Biology at Iowa State University Digital Repository. It has been accepted for inclusion in Ecology, Evolution and Organismal Biology Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Abstract Examining the phenotypic and genetic underpinnings of life-history variation in long-lived organisms is central to the study of life-history evolution. Juvenile growth and survival are often density dependent in reptiles, and theory predicts the evolution of slow growth in response to low resources (resource-limiting hypothesis), such as under densely populated conditions. However, rapid growth is predicted when exceeding some critical body size reduces the risk of mortality (mortality hypothesis).
    [Show full text]
  • 2 Wildebeest in the Serengeti: Limits to Exponential Growth
    Case Studies in Ecology and Evolution DRAFT 2 Wildebeest in the Serengeti: limits to exponential growth In the previous chapter we saw the power of exponential population growth. Even small rates of increase will eventually lead to very large populations if r stays constant. At the beginning of the 19th century Thomas Malthus wrote extensively about the power of exponential growth, pointing out that no population can continue to grow forever. Eventually the numbers of individuals will get so large that they must run out of resources. While Malthus was particularly interested in human populations, the same must be true for all kinds of species. No population can grow exponentially forever. Charles Darwin used those ideas as one of the cornerstones of his theory of natural selection. Because of the speed at which exponentially growing populations can increase in size, very few populations in nature will show exponential growth. Once a population has reached sufficient size to balance the available resource supply, there should be only minor fluctuations in numbers. Only when there is a large perturbation of the environment, such as the introduction of a species to a new area or severe reduction in population size due to hunting or disease will you find populations increasing in an exponential manner. One very well studied system for looking at population dynamics is the wildebeest Figure 2.1. top: Herd of Wildebeest. Bottom: Map (Connochaetes taurinus) on the Serengeti plains of the Serengeti-Mara ecosystem showing the of East Africa. Anthony Sinclair and Simon annual migration route. Mduma from the University of British Columbia have been studying them for 3 decades and have generated a long time series of records of population abundance.
    [Show full text]
  • 1 | Page Names: Activity 1: Population: the Goal of This Activity
    BIO 108-2017 Activity 2- population and community biology Activity 1: population: The goal of this activity is familiarize you with population biology models: In particular: growth models and how they apply to resource management Population Biology: Exponential Growth – 푑푁 = 푟푁 푑푡 This is the most basic population growth model. Growth is dependent on two terms: the existing population (N) and the intrinsic growth rate (r). r is actually a derived and instantaneous rate defined as b-d: birth – death rates. Population Biology: Logistic Growth – 푑푁 퐾 − 푁 = 푟푁( ) 푑푡 퐾 This population growth model has two parts: the left clause is the exponential part and the right clause is a dampening function that introduces density dependence to the model. K in this model is the carrying capacity of the population. Below is the logistic curve for: R=1 Starting population = 2 K=200 1 | P a g e Names: BIO 108-2017 Activity 2- population and community biology The logistic equation shown above is written in its derivative form. Recall from calculus that the second derivative of an equation can be used to determine the minimum and maximum rate of change in a population. The maximum rate of change is the point on the graph above where the population grows fastest. It is the maximum instantaneous slope. Why would we want to know this? Because it has been used as a target for management of harvested species, especially in fisheries. The idea is that harvest of populations to a size equal to the population where growth rate is highest maximizes sustainable harvest.
    [Show full text]
  • Arxiv:2009.11357V3 [Physics.Bio-Ph] 18 Apr 2021 H Rbblt Itiuino H Otrcn Common Recent Most 15]
    Virus-host interactions shape viral dispersal giving rise to distinct classes of travelling waves in spatial expansions 1 1 1, 2 3, 4 1, Michael Hunter, Nikhil Krishnan, Tongfei Liu, Wolfram M¨obius, and Diana Fusco ∗ 1Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom 2Department of Physics, University of Oxford, Oxford, OX1 3PJ, United Kingdom 3Living Systems Institute, University of Exeter, Exeter, EX4 4QD, UK 4Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK (Dated: April 20, 2021) Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit density-dependent dispersal. Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion coefficient akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion.
    [Show full text]
  • Density Dependence and Adult Survival Drive Dynamics in Two High Elevation Amphibian Populations
    diversity Article Density Dependence and Adult Survival Drive Dynamics in Two High Elevation Amphibian Populations Amanda M. Kissel 1,*, Simone Tenan 2 and Erin Muths 3 1 Conservation Science Partners, 11050 Pioneer Trail, Suite 202, Truckee, CA 96161, USA 2 National Research Council, Institute of Marine Sciences (CNR-ISMAR), Arsenale, Tesa 104, Castello 2737/F, 30122 Venezia, Italy; [email protected] 3 U.S. Geological Survey, Fort Collins Science Center, 2150 Centre Ave. Bldg C, Fort Collins, CO 80526, USA; [email protected] * Correspondence: [email protected] Received: 30 October 2020; Accepted: 11 December 2020; Published: 15 December 2020 Abstract: Amphibian conservation has progressed from the identification of declines to mitigation, but efforts are hampered by the lack of nuanced information about the effects of environmental characteristics and stressors on mechanistic processes of population regulation. Challenges include a paucity of long-term data and scant information about the relative roles of extrinsic (e.g., weather) and intrinsic (e.g., density dependence) factors. We used a Bayesian formulation of an open population capture-recapture model and >30 years of data to examine intrinsic and extrinsic factors regulating two adult boreal chorus frogs (Pseudacris maculata) populations. We modelled population growth rate and apparent survival directly, assessed their temporal variability, and derived estimates of recruitment. Populations were relatively stable (geometric mean population growth rate >1) and regulated by negative density dependence (i.e., higher population sizes reduced population growth rate). In the smaller population, density dependence also acted on adult survival. In the larger population, higher population growth was associated with warmer autumns.
    [Show full text]